217. Contains Duplicate

Problem Description

The problem presents us with a task to determine whether an array of integers, nums, contains any duplicate elements. The goal is to return true if any specific value appears at least twice in the array, indicating the presence of duplicates. If every element in the array is unique, we should return false.

Intuition

The intuition behind the solution approach is to utilize a data structure that can handle uniqueness efficiently. A set in Python is a perfect choice for handling unique elements. When we convert the list of numbers into a set, all duplicates are automatically removed because sets cannot contain duplicate elements. Comparing the length of the set with the original list gives us a direct indication of whether there were any duplicates:

1. If there are duplicates in the original list, the set's length will be less because it would have removed the duplicates.
2. If there are no duplicates, both the set and the list will have the same length.

Thus, by checking whether the length of the set is smaller than the length of the original list, we can tell if there are any duplicate numbers in the array. This is a clean and efficient solution as it does not require any additional looping or complex logic.

Learn more about Sorting patterns.

Solution Approach

The implementation of the solution is straightforward and relies on the properties of sets in Python. Here's a step-by-step breakdown of how the solution works:

• We take the input list nums and efficiently convert it into a set using the set() constructor. This process removes any duplicate elements that might be present in the nums list since sets by definition only allow unique elements.

• The operation set(nums) creates a new set containing only unique elements from the original list.

• We then compare the length of the created set with the length of the original nums list using the len() function. The comparison is done by the expression len(set(nums)) < len(nums).

• If the lengths are different, this means the set is shorter because it consolidated duplicate elements from the nums list into single occurrences. Therefore, the original nums list contained duplicates, and we should return true.

• If the lengths are equal, then there were no duplicates to remove when creating the set. This indicates that all elements in the nums list were distinct, so the function should return false.

The given solution is efficient because:

• It uses the property of a set to store unique elements, thus eliminating the need for explicit loops or additional data structures to check for duplicates.

• Conversion from a list to a set and length comparison are operations with a time complexity of O(n), making the entire solution O(n).

• The space complexity of the approach is also O(n) in the worst case, where n is the number of elements in the input list since we might have to store all elements in the set if they are unique.

This one-line solution elegantly solves the problem:

1def containsDuplicate(self, nums: List[int]) -> bool:
2    return len(set(nums)) < len(nums)

Example Walkthrough

Let's assume we are given the following array of integers:

1nums = [1, 3, 4, 2, 3]

We are tasked with finding out if any number appears more than once in the array nums.

Following the solution approach:

1. Convert nums to a set: We first convert the list into a set.

   1unique_nums = set(nums)

   The unique_nums set will be: {1, 2, 3, 4}.

   After this conversion, the set unique_nums contains the numbers {1, 2, 3, 4}. Notice that the duplicate 3 from the original nums list does not appear twice in the set because a set stores only unique values.

2. Compare lengths: We then compare the length of the set unique_nums with the original list nums.

   1Length of nums list: 5
   2Length of unique_nums set: 4

   The length comparison tells us that the set is shorter than the list, indicating duplicates were removed during set conversion.

3. Return true if duplicates exist: Since the lengths aren't equal (the length of unique_nums is less than nums), we determine that duplicates exist in the original list.

   The function using our above method would return true.

For illustration purposes, let's consider another example where nums = [1, 2, 3, 4, 5].

1. Convert nums to a set: Converting nums to a set gives us {1, 2, 3, 4, 5}.

2. Compare lengths: Both the set and the list have a length of 5.

3. Return false if no duplicates: Since the lengths are equal, we can conclude that there are no duplicate values, and our function would return false.

In essence, the function containsDuplicate is effectively checking:

1len(set([1, 3, 4, 2, 3])) < len([1, 3, 4, 2, 3]) # Returns true, duplicates are present
2len(set([1, 2, 3, 4, 5])) < len([1, 2, 3, 4, 5]) # Returns false, no duplicates

Solution Implementation

Time and Space Complexity

The given Python code checks for duplicates in a list by converting it into a set, which stores only unique elements, and then comparing the length of this set to the length of the original list. If the set has fewer elements, it means that there were duplicates in the original list.

Time Complexity:

The main operation here is the conversion of the list into a set, which typically has a time complexity of O(n) where n is the number of elements in the list. This is because the operation needs to iterate through all elements once, adding them into the set and checking for uniqueness.

Space Complexity:

The space complexity is also O(n) in the worst case because in a situation where all elements are unique, the set would need to store all n elements separately from the original list.

Learn more about how to find time and space complexity quickly using problem constraints.